Abstract

This work proposes a simple method, based on the crystal rotation technique and heterodyne interferometry, to simultaneously determine the pretilt angle and cell gap of nematic liquid crystal cells. When heterodyne light passes through a nematic liquid crystal cell, the phase retardation given by the characteristic parameters of the cell can be measured accurately by heterodyne interferometry. This phase retardation relates to the pretilt angle, cell gap, and angle of incidence on the cell. By using the measured phase retardations at two incident angles, the pretilt angle and cell gap of the nematic liquid crystal cell can be estimated by numerical analysis. This method is feasible, requiring only two incident angles and prior knowledge of two characteristic parameters—extraordinary and ordinary refractive indices of the liquid crystal. It is characterized by the advantages of simplicity of installation, ease of operation, high stability, high accuracy, and high resolution.

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References

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  1. T. J. Scheffer and J. Nehring, “Accurate determination of liquid crystal tilt bias angles,” J. Appl. Phys. 48(5), 1783–1792 (1977).
    [CrossRef]
  2. B. L. Van Horn and H. H. Winter, “Analysis of the conoscopic measurement for uniaxial liquid-crystal tilt angles,” Appl. Opt. 40(13), 2089–2094 (2001).
    [CrossRef]
  3. S. J. Hwang, S. T. Lin, and C. H. Lai, “A novel method to measure the cell gap and pretilt angle of a reflective liquid crystal display,” Opt. Commun. 260(2), 614–620 (2006).
    [CrossRef]
  4. I. Dahl, “How to measure the Mueller matrix of liquid-crystal cells,” Meas. Sci. Technol. 12(11), 1938–1948 (2001).
    [CrossRef]
  5. M. H. Smith, “Method and apparatus for determining liquid crystal cell parameters from full Mueller matrix measurements,” US patent No. 7218398 (2007).

2006

S. J. Hwang, S. T. Lin, and C. H. Lai, “A novel method to measure the cell gap and pretilt angle of a reflective liquid crystal display,” Opt. Commun. 260(2), 614–620 (2006).
[CrossRef]

2001

I. Dahl, “How to measure the Mueller matrix of liquid-crystal cells,” Meas. Sci. Technol. 12(11), 1938–1948 (2001).
[CrossRef]

B. L. Van Horn and H. H. Winter, “Analysis of the conoscopic measurement for uniaxial liquid-crystal tilt angles,” Appl. Opt. 40(13), 2089–2094 (2001).
[CrossRef]

1977

T. J. Scheffer and J. Nehring, “Accurate determination of liquid crystal tilt bias angles,” J. Appl. Phys. 48(5), 1783–1792 (1977).
[CrossRef]

Dahl, I.

I. Dahl, “How to measure the Mueller matrix of liquid-crystal cells,” Meas. Sci. Technol. 12(11), 1938–1948 (2001).
[CrossRef]

Hwang, S. J.

S. J. Hwang, S. T. Lin, and C. H. Lai, “A novel method to measure the cell gap and pretilt angle of a reflective liquid crystal display,” Opt. Commun. 260(2), 614–620 (2006).
[CrossRef]

Lai, C. H.

S. J. Hwang, S. T. Lin, and C. H. Lai, “A novel method to measure the cell gap and pretilt angle of a reflective liquid crystal display,” Opt. Commun. 260(2), 614–620 (2006).
[CrossRef]

Lin, S. T.

S. J. Hwang, S. T. Lin, and C. H. Lai, “A novel method to measure the cell gap and pretilt angle of a reflective liquid crystal display,” Opt. Commun. 260(2), 614–620 (2006).
[CrossRef]

Nehring, J.

T. J. Scheffer and J. Nehring, “Accurate determination of liquid crystal tilt bias angles,” J. Appl. Phys. 48(5), 1783–1792 (1977).
[CrossRef]

Scheffer, T. J.

T. J. Scheffer and J. Nehring, “Accurate determination of liquid crystal tilt bias angles,” J. Appl. Phys. 48(5), 1783–1792 (1977).
[CrossRef]

Van Horn, B. L.

Winter, H. H.

Appl. Opt.

J. Appl. Phys.

T. J. Scheffer and J. Nehring, “Accurate determination of liquid crystal tilt bias angles,” J. Appl. Phys. 48(5), 1783–1792 (1977).
[CrossRef]

Meas. Sci. Technol.

I. Dahl, “How to measure the Mueller matrix of liquid-crystal cells,” Meas. Sci. Technol. 12(11), 1938–1948 (2001).
[CrossRef]

Opt. Commun.

S. J. Hwang, S. T. Lin, and C. H. Lai, “A novel method to measure the cell gap and pretilt angle of a reflective liquid crystal display,” Opt. Commun. 260(2), 614–620 (2006).
[CrossRef]

Other

M. H. Smith, “Method and apparatus for determining liquid crystal cell parameters from full Mueller matrix measurements,” US patent No. 7218398 (2007).

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Figures (6)

Fig. 1.
Fig. 1.

Cross section of a nematic liquid crystal cell with pretilt angle α and cell gap d. A beam of light travels through the cell at incident angle φ.

Fig. 2.
Fig. 2.

Measurement of pretilt angle and cell gap of nematic liquid crystal cells.

Fig. 3.
Fig. 3.

Phase retardation versus incident angles of sample S1 at different pretilt angles.

Fig. 4.
Fig. 4.

Error curves of measurements related to pretilt angle α with φ = ± 45°, cell gap d = 5.7μm and the material properties of E7. (a) α = 0–90°; (b) α = 0–9°; (c) α = 11–90°.

Fig. 5.
Fig. 5.

Error curve of measurements as a function of the pretilt angle (α = 0–90°) for an E7 cell. φ= ± 14° and d = 5.7 μm.

Fig. 6.
Fig. 6.

Error curves of measurements. φ = ± 45°, α = 6.73° for an E7 cell.

Tables (1)

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Table 1. Experimental results and reference values.

Equations (7)

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φ=2πdλ[(ne2no2)sinαcosαsinϕno2cos2α+ne2sin2α+nenono2cos2α+ne2sin2α.1sin2ϕno2cos2α+ne2sin2αno2sin2ϕ],
It=Et2=12[1+cos(ωtφ)] ,
Ir=12[1+cos(ωt)] .
φ±ϕ=4πdλ[(ne2no2)sinαcosαsinϕno2cos2α+ne2sin2α].
f(α)=φϕφ±ϕ.
Δα=Δφϕφ±ϕ+Δφ±ϕφϕ+fϕΔϕφ±ϕ2(φϕα)φ±ϕ(φ±ϕα)φϕ,
Δd=Δφϕ+φϕαΔα+φϕϕΔϕφϕd,

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